Generative and probability models of images in problems involving image processing and recognition

This special issue of Opticheskiı˘ Zhurnal is devoted to generative and probability models in problems involving automatic image analysis. These problems are associated with such areas as iconics, image processing, computer vision, pattern recognition, etc., and an extensive and diverse set of methods has been developed in each of these areas that are often applicable only to problems of a definite type. In this connection, it is natural for researchers to strive to develop some generalized approach in terms of which it would be possible to uniformly formulate various problems and to describe methods for solving them.
Even at the stage of conceiving the indicated areas, it was noted that many problems can be formulated as problems of statistical inference. However, such a formulation is not free from the need to develop ad hoc quality criteria of the solution and algorithms for optimizing them, and this often turned out to be less practical than to develop alternative deterministic algorithms.
A new twist in the evolution of the probability approach is associated with developing a theory of so-called graphical models—graphs at whose nodes random quantities are located, while the statistical connections between them are specified by curves. A unified representation of probability models of images and the availability of standard methods of statistical inference based on them became the basis for efficiently solving a definite range of problems involving image processing and recognition. However, graphical models are limited and cannot be used to solve all problems.
At the same time, the success of graphical models in the area of image analysis has attracted attention to probability generative models as a whole, which describe the process of generating certain objects (for example, images) on the basis of the values of quantities that are not directly observable, while the inference on which it is based consists of reconstructing the values of the hidden quantities from the results of observations. An approach based on generative models improves the accuracy of the general probability approach, bringing the development of models to the foreground and separating it from the inference problem.
Such separation eliminates the need to develop deductive algorithms but makes the process of creating new methods less heuristic. Some of the advanced methods in this area were developed partly because of this. For example, one widespread class of deep-learning networks, which now exhibit the best results in a number of image-recognition problems, is based on restricted Boltzmann machines. The Boltzmann machine itself is a generative probability model, but the imposition of definite limitations on its structure makes it possible to infer that it is fairly effective for practical use.
An approach based on generative models has been thoroughly implemented in probability programming in which the programs themselves are the generative models, while general mechanisms of inference from them are built into a language interpreter. Probability programming has begun to be applied to problems of image analysis, although a substantial obstacle here is the inadequate efficiency of common inference mechanisms.
There are still problems, particularly in comparing the images of complex scenes, for which an approach based on generative models does not provide an effective solution. Examples of methods of solving such problems, developed in terms of traditional parameters, are also presented in this issue. Nevertheless, generative probability models are an important component of the methodology of image processing and analysis.